# General algebra

### Factorisation

- The reverse process to expanding is called factorisation. In this case we are given an expression which is a sum of terms and we convert it to a product of two or more terms.
- Expressions may be factorised by removing factors common to two or more terms and then by grouping and if necessary regrouping.
- For example: \(

\newcommand{\eqncomment}[2]{\small{\text{ #2}} }

\newcommand{\ceqns}{\begin{array}{rcll}}

\newcommand{\ceqne}{\end{array}}

\)

\[

\ceqns

&& 3x+3x^2 \\

&=& 3\times x+2x\times x & \eqncomment{0.4}{where \(x\) is the common factor} \\

&=& x(3+2x)

\ceqne

\] - Another example of factorising:

2x^{3} +4x^{2}+6x = 2x(x^{2}+2x+3)

\end{eqnarray}

where \(2x\) is the common factor.